
Cubical boxes of volume $15625c{m^3}$ each are put in a cubical store of side $2.5m$
I) How many such boxes can be put in the stores?
II) What are the dimensions of the box?
A) $(i)1250(ii)15cm$
B) $(i)1000(ii)15cm$
C) $(i)1250(ii)25cm$
D) $(i)1000(ii)25cm$
Answer
459.3k+ views
Hint: Here we will use some formula for calculating the number of boxes in given square feet and the dimensions of the box
for given questions. This two information is already given this question using formula and substitute the values and find the
answer.
Formula used: Dimension of box $ = {(side)^3}$
Number of boxes that store can contain $ = \dfrac{{{\text{Volume of cubical store}}}}{{{\text{Volume of 1 box}}}}$
Complete step-by-step solution:
In given in the question is
Volume of the boxes = $15625c{m^3}$
Side of cubical store $2.5m = 2.5 \times 100cm = 250cm$ (We will change the meter to centimeter we will multiply $100$ )
Volume of cubical store $ = {(side)^3} = {(250)^3} = 15625000c{m^3}$
Thus, number of boxes that store can contain $ = \dfrac{{{\text{Volume of cubical store}}}}{{{\text{Volume of 1 box}}}} =
\dfrac{{15625000}}{{15625}} = 1000$
Dimension of the box $ = 15625c{m^3}$
$
\Rightarrow sid{e^3} = 15625c{m^3} \\
\Rightarrow side = \sqrt[3]{{15625c{m^3}}} = \sqrt[3]{{25 \times 25 \times 25c{m^3}}} = 25cm
$
Side of the box is $ = 25cm$
Here the answer will be option D $1000,25cm$
Note: A cube is $3$ dimensional shape with $6$ equal sides, $6$ faces and $6$ vertices. Each face of a cube is a square. In $3$
dimension, the sides of a cube are, the length, width and the height. The volume of a solid cube is the amount of space
occupied by the solid cube. For a hollow cube, the volume is the difference in space occupied by the cube and amount of
space inside the cube.
Identify the length of side or length of the edge. Multiply the length by itself three times. Write the result accompanied by
the units of volume. Volume is measured in cubic units. Cubic meters $({m^3})$ ,cubic centimeters $(c{m^3})$ The volume
can also be measured in liters or milliliters.
for given questions. This two information is already given this question using formula and substitute the values and find the
answer.
Formula used: Dimension of box $ = {(side)^3}$
Number of boxes that store can contain $ = \dfrac{{{\text{Volume of cubical store}}}}{{{\text{Volume of 1 box}}}}$
Complete step-by-step solution:
In given in the question is
Volume of the boxes = $15625c{m^3}$
Side of cubical store $2.5m = 2.5 \times 100cm = 250cm$ (We will change the meter to centimeter we will multiply $100$ )
Volume of cubical store $ = {(side)^3} = {(250)^3} = 15625000c{m^3}$
Thus, number of boxes that store can contain $ = \dfrac{{{\text{Volume of cubical store}}}}{{{\text{Volume of 1 box}}}} =
\dfrac{{15625000}}{{15625}} = 1000$
Dimension of the box $ = 15625c{m^3}$
$
\Rightarrow sid{e^3} = 15625c{m^3} \\
\Rightarrow side = \sqrt[3]{{15625c{m^3}}} = \sqrt[3]{{25 \times 25 \times 25c{m^3}}} = 25cm
$
Side of the box is $ = 25cm$
Here the answer will be option D $1000,25cm$
Note: A cube is $3$ dimensional shape with $6$ equal sides, $6$ faces and $6$ vertices. Each face of a cube is a square. In $3$
dimension, the sides of a cube are, the length, width and the height. The volume of a solid cube is the amount of space
occupied by the solid cube. For a hollow cube, the volume is the difference in space occupied by the cube and amount of
space inside the cube.
Identify the length of side or length of the edge. Multiply the length by itself three times. Write the result accompanied by
the units of volume. Volume is measured in cubic units. Cubic meters $({m^3})$ ,cubic centimeters $(c{m^3})$ The volume
can also be measured in liters or milliliters.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Science: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Class 9 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell

What is pollution? How many types of pollution? Define it

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Distinguish between Conventional and nonconventional class 9 social science CBSE
